Thirty six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters and so on. Work out the number of scooters in the second half of the row.

Options

A. 10
B. 12
C. 15
D. 17

Explanation

To solve the problem, we need to determine how many scooters are parked in the second half of the row of vehicles. Let's break it down step by step.

### Step 1: Understand the arrangement of vehicles
We know that there are 36 vehicles in total, consisting of cars and scooters. The arrangement is such that after the first car, there is 1 scooter; after the second car, there are 2 scooters; after the third car, there are 3 scooters, and so on.

### Step 2: Identify the pattern
The pattern of vehicles can be represented as follows:
- After the 1st car (C1), there is 1 scooter (S1).
- After the 2nd car (C2), there are 2 scooters (S2, S3).
- After the 3rd car (C3), there are 3 scooters (S4, S5, S6).
- After the 4th car (C4), there are 4 scooters (S7, S8, S9, S10).
- This pattern continues until we reach the 8th car.

### Step 3: Calculate the total number of vehicles used
We can calculate how many vehicles are used up to the 8th car:
- C1 + S1 = 2 vehicles
- C2 + S2 + S3 = 3 vehicles
- C3 + S4 + S5 + S6 = 4 vehicles
- C4 + S7 + S8 + S9 + S10 = 5 vehicles
- C5 + S11 + S12 + S13 + S14 + S15 = 6 vehicles
- C6 + S16 + S17 + S18 + S19 + S20 + S21 = 7 vehicles
- C7 + S22 + S23 + S24 + S25 + S26 + S27 + S28 = 8 vehicles
- C8 + S29 + S30 + S31 + S32 + S33 + S34 + S35 + S36 = 9 vehicles

### Step 4: Count the total vehicles used
Adding these together:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 vehicles.

However, we only have 36 vehicles in total. This means we can only park up to the 8th car.

### Step 5: Determine the number of scooters in the first half
From the arrangement, we can see that:
- The first half of the row consists of vehicles from position 1 to 18.
- The 8th car is at position 17, and it has 8 scooters after it.

### Step 6: Count the scooters in the second half
The second half of the row consists of vehicles from position 19 to 36. Since we have 36 vehicles total and the first half ends at position 18, we need to find out how many scooters are in positions 19 to 36.

The remaining vehicles will be:
- C9 (the 9th car) will be parked at position 19, and it will have 9 scooters after it (positions 20 to 28).
- C10 (the 10th car) will be parked at position 29, and it will have 10 scooters after it (positions 30 to 39).

Since we only have 36 vehicles, we can only consider the first 8 cars and their respective scooters.

### Step 7: Count the scooters in the second half
From the arrangement:
- The scooters from the 9th car (C9) and onwards are not counted because they exceed the total number of vehicles.

Thus, the scooters in the second half (positions 19 to 36) will be the scooters from the 8th car and the 9th car, which are:
- 9 scooters from the 9th car (positions 20-28).
- 10 scooters from the 10th car (positions 30-39).

However, since we only have 36 vehicles, we can only count the scooters up to position 36, which means we will have 9 scooters from the 9th car and 7 scooters from the 10th car.

### Final Count
Therefore, the total number of scooters in the second half (positions 19 to 36) is:
- 9 (from C9) + 7 (from C10) = 16 scooters.

### Conclusion
The number of scooters in the second half of the row is **16**.

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